Question

1. 29° 12 x

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 29^{\circ}\), the opposite side to the \(29^{\circ}\) angle is \(12\), and the hypotenuse is \(x\). So, \(\sin29^{\circ}=\frac{12}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation \(\sin29^{\circ}=\frac{12}{x}\) as \(x=\frac{12}{\sin29^{\circ}}\).
We know that \(\sin29^{\circ}\approx0.4848\). Then \(x=\frac{12}{0.4848}\approx24.75\).

Answer:

\(x\approx24.75\)